Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 897279, 11 pages
doi:10.1155/2010/897279
Research Article

On The Frobenius Condition Number of Positive Definite Matrices

Ramazan Türkmen and Zübeyde Ulukök

Department of Mathematics, Science Faculty, Selçuk University, 42003 Konya, Turkey

Received 19 February 2010; Revised 4 May 2010; Accepted 15 June 2010

Academic Editor: S. S. Dragomir

Copyright © 2010 Ramazan Türkmen and Zübeyde Ulukök. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present some lower bounds for the Frobenius condition number of a positive definite matrix depending on trace, determinant, and Frobenius norm of a positive definite matrix and compare these results with other results. Also, we give a relation for the cosine of the angle between two given real matrices.